A three-way consensus model with regret theory under the framework of probabilistic linguistic term sets

For multi-attribute group decision-making (MAGDM) problems, this paper proposes a three-way consensus model based on regret theory (RT) under the framework of probabilistic linguistic term sets (PLTSs), i.e., the PL-RT-GTWD model. Specifically, the PL-RT-GTWD model mainly consists of the following two components: (1) The consensus measurement considering the relativity among decision-makers (DMs); (2) A three-way consensus feedback mechanism with the minimum adjustment. First, the relative relationship between DMs is supplemented, and the consensus degree of the DM evaluation matrix is measured by a newly developed distance measure. Second, an optimization model with the minimum adjustment for all DMs to modify and reach the final desired goal (group consensus opinions) is constructed, so that DMs can achieve a balance between reaching consensus and maintaining individual independence. Then, taking the minimum adjustment before and after the adjustment as the objective function, the increase of consensus degrees and the initial range of adjustment parameters as constraints, the goal programming on adjustment parameters is constructed. It is noteworthy that the initial range of adjustment parameters is divided via three-way decision (TWD) tools that consider the regret generated during the adjustment, so as to avoid the subjectivity of the adjustment and reduce adjustment costs. Finally, comparative and sensitivity analyses are carried out to verify the feasibility and superiority of the constructed model.